Combined, there are Asians, Africans, Europeans, and Americans in a village. The number of Asians exceeds the number of Afric
1 answer:
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Statement Problem: P, Q and R are three buildings. A car began its journey at P, drove to Q, then to R and returned to P. The bearing of Q from P is 058° and R is due east of Q. PQ = 114 km and QR = 70 km. ( Draw a clearly labelled diagram to represent the above information.
Solution:
Answers:
These are the statements that apply:
The initial value is 3.
The range is y >0.
The simplified base is 8.
Explanation:
1) Given expression:
2) Check every statement:
a) The initial value is 3?
initial value ⇒ x = 0 ⇒
∴ The statement is right.
b) The initial value is 48?
Not, as it was already proved that it is 3.
c) The domain is x > 0?
No, because the domain of the exponential functions is all the Real numbers.
d) The range is y > 0?
That is correct, the exponential function is continuous, and monotonon increasing.
The limit when x → - ∞ is zero, but y never reaches zero, and the limit when x → ∞ is + ∞, meaning that the range is y > 0.
e) The simplified base is 12?
This is how you simplify the base:
Which shows that the simplified base is 8 (not 12).
f) The simplified base is 8?
Yes; this was just proved.
Let the smaller number be x.
Given, the larger number is 7 times the smaller number.
So, the larger number = 7x.
Given, 3 times the larger number is 7 more than 4 times the smaller number.
So we can write the equation as,
Now we have to move 4x to the left side by subtracting 4x from both sides.
To get x, we will divide both sides by 17. We will get,
So the smaller number =
The larger number = =
So we have got the required numbers.
Smaller number = and larger number =
.